(a)
\Find the zeros of on the interval
.
The function is .
Find the zeros of by equating
to zero.
The general solution of is
, where
is an integer.
The general solutions is , where
is an integer.
If , then
and
and
.
If , then
and
.
If , then
and
and
.
If , then
and
and
.
Therefore, the zeros of on the interval
are
,
,
,
,
and
.
(b)
\The function is and the interval is
.
Rewrite the function as .
Make a table to find the ordered pairs.
\Choose different values of on the interval
, then find corresponding values for
.
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Draw a coordinate plane.
\Plot the points obtained in the above table.
\Connect those points with a smooth curve.
\Graph :
\(c)
\Solve in the interval
.
The general solution of is
, where
is an integer.
The general solutions is , where
is an integer.
If , then
and
.
If , then
and
.
If , then
and
and
.
If , then
and
and
.
Therefore, the solutions of on the interval
are
,
,
,
,
and
.
For the solutions of find corresponding values for
.
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Therefore, the points on the graph of are
,
,
,
,
, and
.
Take the graph drawn in part (b).
\Label the points obtained in the above table.
\Graph :
\.
(d)
\Observe the graph drawn in part (b) along with the results of part (c) :
\The values of such that
on the interval
are
.
(a)
\The zeros of on the interval
are
,
,
,
,
and
.
(b)
\Graph of :
(c)
\The points on the graph of are
,
,
,
,
, and
.
Graph :
\(d)
\.